Impact of Radio Irregularities on Connectivity of Wireless Networks with Log-normal Shadowing

To better understand connectivity of multihop wireless networks with the log-normal shadowing, we study the impact of radio irregularities on network connectivity under such a realistic shadowing model. Existing results indicate that connectivity increases when the radio propagation becomes more irregular. But all of these results were only based on simulation studies or the assumption that the important boundary effect is ignored to avoid the challenging technical analysis. Therefore, they can hardly be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. In this paper, we assume the wireless nodes are represented by a Poisson point process with density n over a unit-area disk. With the boundary effect taken into consideration, we prove analytically that network connectivity increases when the radio propagation becomes more irregular (i.e., the shadowing deviation increases) under such a realistic shadowing model.